The H\"older-Poincar\'e Duality for Lq,pL_{q,p}-cohomology

We prove the following version of Poincare duality for reduced $L_{q,p}$-cohomology: For any $1<q,p<\infty$, the $L_{q,p}$-cohomology of a Riemannian manifold is in duality with the interior $L_{p',q'}-cohomology for$1/p+1/p'=1$,$1/q+1/q'=1$.Comment: 21 page

Phonon Raman spectra of colloidal CdTe nanocrystals: effect of size, non-stoichiometry and ligand exchange

Resonant Raman study reveals the noticeable effect of the ligand exchange on the nanocrystal (NC) surface onto the phonon spectra of colloidal CdTe NC of different size and composition. The oleic acid ligand exchange for pyridine ones was found to change noticeably the position and width of the longitudinal optical (LO) phonon mode, as well as its intensity ratio to overtones. The broad shoulder above the LO peak frequency was enhanced and sharpened after pyridine treatment, as well as with decreasing NC size. The low-frequency mode around 100 cm-1 which is commonly related with the disorder-activated acoustical phonons appears in smaller NCs but is not enhanced after pyridine treatment. Surprisingly, the feature at low-frequency shoulder of the LO peak, commonly assigned to the surface optical phonon mode, was not sensitive to ligand exchange and concomitant close packing of the NCs. An increased structural disorder on the NC surface, strain and modified electron-phonon coupling is discussed as the possible reason of the observed changes in the phonon spectrum of ligand-exchanged CdTe NCs

Micro-Raman and micro-transmission imaging of epitaxial graphene grown on the Si and C faces of 6H-SiC

Micro-Raman and micro-transmission imaging experiments have been done on epitaxial graphene grown on the C- and Si-faces of on-axis 6H-SiC substrates. On the C-face it is shown that the SiC sublimation process results in the growth of long and isolated graphene ribbons (up to 600 μm) that are strain-relaxed and lightly p-type doped. In this case, combining the results of micro-Raman spectroscopy with micro-transmission measurements, we were able to ascertain that uniform monolayer ribbons were grown and found also Bernal stacked and misoriented bilayer ribbons. On the Si-face, the situation is completely different. A full graphene coverage of the SiC surface is achieved but anisotropic growth still occurs, because of the step-bunched SiC surface reconstruction. While in the middle of reconstructed terraces thin graphene stacks (up to 5 layers) are grown, thicker graphene stripes appear at step edges. In both the cases, the strong interaction between the graphene layers and the underlying SiC substrate induces a high compressive thermal strain and n-type doping

Dielectric enhancement of excitons in semiconducting quantum wires

The energy of the exciton ground state in a semiconducting cylindrical quantum wire surrounded by a dielectric has been calculated using a variational technique accounting for the effect of dielectric enhancement. The effect of dielectric enhancement in such a system has been clearly demonstrated. Exciton parameters have been calculated for an intercalated leadiodide-based quasi-one-dimensional semiconductor and GaAs wires in asbestos nanotubes